1. Solving Equations with variables on both sides of the Equals
Chapter 3.5

2. Solving Equations with variables on both sides of the Equals
Lesson Objective: NCSCOS Use linear functions to model and solve problems
Students will know how to solve equations with variables on both sides.
Students will know how to use the distributive property to solve problems.
Students will know how to combine like terms to solve problems

3. Solving Equations with variables on both sides of the Equals5x
- 8 = 3x + 12
Example 1:
First we must get all the variables on one side of the equation.
Subtract 3x from both sides
-3x x 2x
- 8 = 12

4. 2x
- 8 = 12 2
x = 20
x = 10
Second we have to get all the numbers on the other side
Add 8 to both sides
Divide both sides by 2

5. Solving Equations with variables on both sides of the Equals
6 – x = 5x + 30
5y – 2y = 3y + 2
4m – 8 = 10 – 2m
8 + 4k = k
(2/5)x – 8 = 9 – (3/5)x
Practice

6. Solving Equations with variables on both sides of the Equals
Example 2:
Distribute on both sides
Add 10x to both sides
4(2x – 1) = -10(x – 5)
8x – 4 = -10x + 50
+10x x
18x – 4 = 50

7. Solving Equations with variables on both sides of the Equals
Add 4 to both sides
Divide by 18
18x – 4 = 50
18x = 54
x = 3

8. Solving Equations with variables on both sides of the Equals
-3(x + 5) = 3(x – 1)
5(x + 2) = 2(3 – x)
4(m + 3) = 36
4(y – 2) = 2(5 – y)
3(x – 8) = 3x
More Practice

9. Solving Equations with variables on both sides of the Equals
Example 3:
Distribute on both sides
Combine like terms on either side of the equals sign
5(x + 3) + 9 = 3(x – 4) + 6
5x = 3x –
5x + 24 = 3x - 6

10. Solving Equations with variables on both sides of the Equals
Subtract 3x from both sides
Add 24 to both sides
Divide by 2
5x + 24 = 3x - 6
2x + 24 = -6
2x = -30
x = -15

11. Solving Equations with variables on both sides of the Equals
3(x – 8) – 5 = 9(x + 2) + 1
2(x + 2) + x = 5 + 4(x – 2)
5x – (3x – 3) = 2x + 3(x + 4)
Last Practice!

12. Solving Equations with variables on both sides of the Equals
Quiz 3.5
2x + 3 = 3x – 5
7x – 3 = 3 – 2x
2(x + 3) = 3(x – 4)
5(2x – 4) = -6(2 – x)
3(x + 2) – 2x = 4(x -3) + 6